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Question Number 73485 by abdomathmax last updated on 13/Nov/19

find the roots of P(x)=(1+ix +jx^2 )^n −1  with j =e^(i((2π)/3))    then factorize P(x) inside C[x]  decompose the fraction F=(1/P)

$${find}\:{the}\:{roots}\:{of}\:{P}\left({x}\right)=\left(\mathrm{1}+{ix}\:+{jx}^{\mathrm{2}} \right)^{{n}} −\mathrm{1} \\ $$$${with}\:{j}\:={e}^{{i}\frac{\mathrm{2}\pi}{\mathrm{3}}} \:\:\:{then}\:{factorize}\:{P}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$${decompose}\:{the}\:{fraction}\:{F}=\frac{\mathrm{1}}{{P}} \\ $$

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